The graph shown is a parabola opening upwards, which indicates a quadratic function with a minimum value at its vertex. Observing the graph, we see that the vertex, which is the lowest point of the parabola, lies at the origin $(0, -10)$.

Thus, the minimum value of this function is: $-10$

Would you like further details or have any questions?

Here are five related questions that could expand on this topic:

1. What is the general form of a quadratic function, and how can it help identify the vertex?
2. How can we determine the minimum or maximum value of a quadratic function algebraically?
3. What are the implications of the direction (upward or downward) of a parabola on its minimum or maximum value?
4. How would the minimum value change if the function is vertically shifted?
5. How can transformations affect the vertex of a quadratic function?

Tip: For any parabola, if the coefficient of $x^2$ is positive, the graph opens upward and has a minimum point. If it’s negative, the graph opens downward and has a maximum point.